Bayesian Methods for Causal Effect Estimation

2026 CSSC Scientific Workshop

Instructor: Kuan Liu, University of Toronto
Date: May 30, 2026
Duration: 50 minutes

---

Workshop Overview

Bayesian methods offer several practical advantages for causal inference: they provide a natural way to quantify uncertainty in causal effect estimates and allow us to assess sensitivity to violations of key causal assumptions. Despite these advantages, Bayesian causal inference remains underused in practice and is rarely covered in introductory causal inference courses.

This workshop bridges that gap and is suitable for anyone with familiarity with regression and Bayesian modeling. No prior exposure to causal inference is required.

Working through simulated and real data examples in R, we cover:

• Bayesian g-computation
• Bayesian propensity score weighting
• Bayesian marginal structural models for time-varying treatments
• Bayesian sensitivity analysis for unmeasured confounding (latent variable approach)
• Bayesian causal forests for heterogeneous treatment effects (time permitting)

---

Repository Structure

.
├── bayesian_causal_workshop.qmd   # Quarto slide deck (revealjs)
├── index.qmd                      # Workshop index page
├── style.css                      # Custom CSS for slide formatting
├── workshop_code.R                # Standalone R code
├── continuous_outcome_data.csv    # Simulated longitudinal data
├── figures/                       # Output plots (generated by running R scripts)
├── 2026CSSC_BayesianCausal.Rproj  # RStudio project file
└── README.md                      # This file

---

Data

RHC Dataset (Right Heart Catheterization)

Used for all point-treatment examples (Parts II, IV, V).

• Source: Connors et al. (1996), publicly available at https://hbiostat.org/data/repo/rhc.csv
• N: 5,735 critically ill ICU patients
• Treatment: Right heart catheterization in first 24 hours (swang1)
• Outcomes: 30-day mortality (death), hospital length of stay
• Confounders: Age, sex, race, disease category, vital signs, lab values

The data is loaded directly from the URL in the R script — no download needed.

Simulated Longitudinal Data (continuous_outcome_data.csv)

Used for the time-varying treatment example (Part III).

• N: 1,000 subjects, 2 visits
• Variables: Baseline covariates (w1, w2), time-varying confounders (L1_1, L2_1, L1_2, L2_2), binary treatments (a_1, a_2), continuous outcome (y)
• Causal estimand: ATE of always treated ($\bar{a}=1$) vs never treated ($\bar{a}=0$)

---

Methods Covered

Part	Method	R Package	Outcome	Time-varying
II	Parametric Bayesian g-computation	rstanarm	Binary	No
II	Nonparametric Bayesian g-computation (BART)	BART	Binary	No
II	Bayesian propensity score weighting	rstanarm	Binary	No
III	Bayesian marginal structural model	bayesmsm	Continuous	Yes
IV	Bayesian sensitivity analysis (latent $U$)	rstan	Binary	No
V	Bayesian causal forests (CATE)	bcf	Binary	No

---

Getting Started

1. Install required R packages

install.packages(c(
  "tidyverse",
  "rstanarm",
  "rstan",
  "BART",
  "bcf",
  "bayesmsm",
  "gtools"
))

Note on rstan: If you have not used Stan before, follow the RStan Getting Started guide to configure your C++ toolchain before installing.

2. Clone this repository

git clone https://github.com/Kuan-Liu-Lab/2026CSSC_BayesianCausal.git
cd 2026CSSC_BayesianCausal

3. Run the workshop code

Open the project by double-clicking 2026CSSC_BayesianCausal.Rproj in RStudio. This sets the working directory automatically so all file paths resolve correctly.

source("workshop_code.R")

---

Selected References

• Oganisian, A. & Roy, J.A. (2021). A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches. Statistics in Medicine, 40(2), 518–551.
• Oganisian, A. (2026). Bayesian sensitivity analyses in causal inference. arXiv:2602.23640.
• Saarela, O. et al. (2015). On Bayesian estimation of marginal structural models. Biometrics, 71(2), 279–288.
• Liu, K. et al. (2020). Estimation of causal effects with repeatedly measured outcomes in a Bayesian framework. Statistical Methods in Medical Research, 29(9), 2507–2519.
• Hahn, P.R., Murray, J.S., & Carvalho, C.M. (2020). Bayesian regression tree models for causal inference: Regularization, confounding, and heterogeneous treatment effects. Bayesian Analysis, 15(3), 965–1056.
• Chipman, H.A., George, E.I., & McCulloch, R.E. (2010). BART: Bayesian additive regression trees. Annals of Applied Statistics, 4(1), 266–298.
• Rubin, D.B. (1981). The Bayesian bootstrap. Annals of Statistics, 9(1), 130–134.
• Connors, A.F. et al. (1996). The effectiveness of right heart catheterization in the initial care of critically ill patients. JAMA, 276(11), 889–897.

---

License

This workshop material is made available for educational purposes.
© 2026 Kuan Liu, University of Toronto.